Feedback stabilization and Lyapunov functions

F.H. Clarke (1) , Yury Ledyaev , Ludovic Rifford (2) , R.J. Stern

1 ICJ - Institut Camille Jordan
2 JAD - Laboratoire Jean Alexandre Dieudonné

Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A further result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish a robustness property of the feedback relative to measurement error commensurate with the sampling rate of the control im- plementation scheme.

Domaines: Optimisation et contrôle [math.OC]

F.H. Clarke, Yury Ledyaev, Ludovic Rifford, R.J. Stern. Feedback stabilization and Lyapunov functions. SIAM Journal on Control and Optimization, 2000, 39 (1), pp.25-48. ⟨hal-00768992⟩